Consider a closed economy in which the population grows at the rate of 1% per year. The per-worker production function is y = 6√c, where y is output per worker and k is capital per worker. The depreciation rate of capital is 14% per year.
a. Households consume 90% of income and save the remaining 10% of income. There is no government spending. What are the steady-state values of capital per worker, output per worker, consumption per worker, and investment per worker?
b. Suppose that the country wants to increase its steady-state value of output per worker. What steady-state value of the capital-labour ratio is needed to double the steady-state value of output per worker? What fraction of income would households have to save to achieve a steady-state level of output per worker that is twice as high as in part(a)?